A tree based lack-of-fit test for multiple logistic regression

Area of Science:

• Statistics
• Biostatistics
• Epidemiology

Background:

• Assessing the fit of regression models is crucial in statistical analysis.
• Existing lack-of-fit tests often focus on simple regression and may not be valid for multiple logistic regression with continuous covariates.

Purpose of the Study:

• To develop and evaluate a novel tree-based test for assessing the lack-of-fit in multiple logistic regression models.
• To provide a more powerful alternative to existing methods, particularly when continuous covariates are present.

Main Methods:

• A recursive partitioning algorithm is employed to divide the sample space into distinct groups.
• The proposed test statistic is based on grouping observations, similar to the Hosmer and Lemeshow approach, but without relying on probabilities fitted under the null model.
• Simulations and data examples are used for comparison with other tests.

Main Results:

• The proposed tree-based lack-of-fit test demonstrates potentially more powerful assessment of model fit compared to traditional methods.
• Comparisons with the Hosmer and Lemeshow test and other lack-of-fit tests are illustrated through simulations and real-world data.

Conclusions:

• The proposed recursive partitioning-based grouping strategy offers a promising approach for evaluating multiple logistic regression model fit.
• This method enhances the assessment of model adequacy, especially in the presence of continuous covariates, providing a valuable tool for researchers.